1. **State the problem:** We are given probabilities for events A and B: $P(A) = 0.6$, $P(A \cap B) = 0.2$, and $P(A \cup B) = 0.9$. We need to find $P(B)$. 2. **Recall the formula for the union of two events:** $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ This formula accounts for the overlap between A and B to avoid double counting. 3. **Substitute the known values into the formula:** $$0.9 = 0.6 + P(B) - 0.2$$ 4. **Simplify the equation:** $$0.9 = 0.4 + P(B)$$ 5. **Isolate $P(B)$:** $$P(B) = 0.9 - 0.4$$ 6. **Calculate the value:** $$P(B) = 0.5$$ **Final answer:** $$\boxed{0.5}$$